The power of form applied to geometric tracery : one hundred designs and their foundations resulting from one diagram

THE

POWER OF FORM

APPLIED TO

Digitized by the Internet Archive
in 2014

https://archive.org/details/powerofformappliOObill_0

' THE

POWER OF FORM

APPLIED TO

GEOMETRIC TRACERY.

RESULTING FROM

iicgram.

By ROBERT WILLIAM BILLINGS, Architect,

ASSOCIATE OP THE INSTITUTE OP BRITISH ARCHITECTS,
AND

HONORARY MEMBER OP THE SOCIETY OP ANTIQUARIES OP SCOTLAND.

PUBLISHED FOR THE AUTHOR

BY

"WILLIAM BLACKWOOD AND SONS,

45, GEORGE STREET, EDINBURGH;
AND 37, PATERNOSTER ROW, LONDON.
1851.

PREFACE.

The Author of this treatise was first in the field to prove^
that not only was the whole detail of Gothic Architecture
founded upon g'eometric law^ but that the power of desig-n
still remained with us^ waiting* only for its application. In
addressing* himself to the learner^ for whose especial use his
labours here are intended^ he does not wish for one moment
to question the previous knowledg-e upon this subject possessed
by many practised Architects^ who must have travelled over
the same g-round as himself in searching* for the primary
elements of their profession.

But whatever the knowledg*e of others may have been
upon our present subject^ it has not been g-iven to the world^
and the Author's claim holds g*ood as the orig-inator of the
conjurations embodied here and in other workS; and which^
like all sleight-of-hand tricks^ are very easy. In short
everybody can do them — that is^ when they know how.

The g*eneral circulation of works on art has been limited
by the high price demanded in return for costly production^
and thus their g*eneral g'ood has been all but lost^ because
their purchase has been beyond the means of those for whom
they were intended. In extenuation of this unfortunate
position^ it must be admitted that^ unlike the works of writers^

A 2

vi

PEEFACE.

their expense is not limited by merely transferring* the labours
of the brain to the types of the printer^ for there is drawing*^
expensive eng^raving*^ and the g*reat cost of printing* from
copper or steel plates.

For the first time^ during- a career of some experience in
the publication of architectural works^ the producer has
chang-ed his tactics^ to meet^ if possible^ the case he has
stated. His drawing's have been engraved on wood^ by his
friend Eobert E. Branston^ whose known ability^ both as an
artist and a man of business^ needs no eulog-ium here.

The cost of wood block engraving's is upon a par with
that of plates ; but here all comparison ends ; and the mere
question of paper and print has enabled the Author to place
the results of his labour within the means of all who may be
interested in the principles he has endeavoured to embody.

And thus his volume^ possessing* possibly as much novelty
as many romances of the day^ is produced with all the cost of
illustration^ at a less cost to the public than is usually made
for a single volume of that class.

St. Mart's Eoad,

Canonbuet, London.
January y 1851.

To the Student^ in his just desire to cultivate the Art of
Design^ and to those whose hands fashion the creations
of the Artist^ a new series of leaves upon one of its
branches cannot fail to be of immediate interest; and^ were
the motive power of Art unanimous upon its advance^ our
preliminary Essay upon the illustrations comprising* the
present book^ would be necessarily short — our road would
indeed be pleasant travel^ for we should be sure of a
reception as the possible contributor of new stores to its
ever varying- wants. But we have^ unfortunately^ to regret
that there is a class^ and that a very numerous one^ who
act in all matters concerning- Architecture^ and the Arts sub-
servient to it^ as thoug-h every thing- had been accomplished^
that nothing- remained for the present or future ag-es of
Architects and Artists g-enerally^ but to be continually
jumbling- tog-ether the productions of their forefathers^ and
then to dig-nify them with the title of Desig-ns. We can
thus fancy the dismay of our mere antiquity-lovers'^ at
the announcement of an extension of the field of desig-n^
entered by means of that which is known as the Gothic style.

Opposed to the neg-ative state of art we have described^
and protesting- most emphatically against the fettering-^ nay,

8

of absolutely staying* prog-ress in any branch of knowledg-e
by slavish adhesion to mere precedent^ we venture to place
before the world a production^ claiming' (although by merely
playing- with compasses)^ that much to be desired qualification^
orig-inality. Fancied inventors of a theme are g-enerally
enthusiasts upon their subject^ and doubtless the Author of
the present attempt will be pronounced one^ when he
ventures to describe it as the re-opening* of a shaft to the
mine of ornamentation^ which at the very surface has pierced
a vein it will be indeed difficult to exhaust in the working*.
Nay^ in the experience g-ained by practice^ he goes further,
and asserts the impossibility of accomplishing* such a task;
for to the skilled artist there is no more difficulty in exhibiting*
new combinations of form than is experienced by the musical
composer in producing* chang*es of sound, or by the arith-
metician in varying* the power of numbers.

It may be repeated, that there is no real difficulty ; and
further, that an advance as palpable as its hitherto admitted
retrogression, would have been made in Architecture, as time
has produced in other Arts, had the forward movement not
been stopped by that ex;treme veneration for antiquity, which
has reached such an absurd point, as to declare all prog-ress
at an end — that the modern race of Architects are only
to retail the wealth already created, and not to gather for
themselves fi^esh stores from the ever increasing fields of
knowledge. It is fortunate, however, for Art, that there
are other classes, deeply interested in its progress, and
it is to them we would address the few words elucidatorv of
the object of our work, and by way of introduction to

the Desig-ns^ which can be read without the aid of any very
voluminous essay. Indeed^ it may be fairly asked whether
they require an essay^ for their true reading' is arrived at by
the mere use of a pair of compasses.

The more we examine the powers of Desig'n developed by
the aid oijixed diagrams^ or foundations^ the more absurd does
it appear^ that ever since the revival of Gothic Architecture
we should have g*one on for ever copying* — taking* it for
g-ranted as a preliminary that all possible combinations were
exhibited in the works of our predecessors ; considering*^ in
shorty that the mine was exhausted_, that the works completed
some hundreds of years since were a "finality/' when in
fact^ and notwithstanding* all that the ancient Architects
accomplished in the field of decorative desig*n^ they scarcely
explored its boundary^ while the vast and unlimited space
lying* beyond is still untrodden. So g'reat^ indeed^ is the
power of this mechanical field of Art^ and so simple its
cultivation^ that it is absolutely easier to produce new
combinations than to copy old ones. Of this fact there can
be no doubt^ and any Artist may prove it by the most
cursory study of the subject ; but beyond the mere saving*
of absolute labour in production^ and far above the mere
credit due to the most exquisite copy^ there is the satisfaction
and the pride all men should feel when they have produced
an original instead of a repetition^ and this^ by simply
adhering to the same unerring* law^s of truth which g*uided the
medieval artists in their productions.

Every eye admires the wonderfully elaborated screen-
work^ the g'org'eous windows of " airy tracery/' (whose frag*ile

10

appearance would almost seem to contradict an existence of
centuries)^ the intricate network enveloping* many of the
mag-nificent towers of the Continental Cathedrals^ and in
some cases those of our own land • and why should we not
inherit the spirit which animated their Architects ? There is
no m5^stery about the matter^ for all are desig'ned upon the
most simple of g"eometric laws^ as palpable now as they
were of old. Shall we not therefore be permitted to make use
of these laws^ when it is known that combinations innume-
rable may be produced ? Shall our orig-inal desig-ns not be
allowed to stand on their own merits side by side with the
emanations of our forefathers ?

We advocate the extension of knowledg-e by their
experience ; we urg-e the attainment of their spirit — but
while admiring- beyond measure their beauties^ we protest
ag-ainst mere copyism of their works^ as fatal to progression
in Art^ and as rendering" the would-be Artist essentially
a mechanic^ whether he be a Painter^ a Sculptor^ or an
Architect. Painters do not permit the admirers of pictures to
reduce their art to this deg-raded state^ neither do Sculptors
rise as mere adaptors of former works^ or^ speaking* plainly^
as mechanics — why then should the professor of the noble
art of Architecture (without whose protection not one of the
sister arts would be able to preserve their productions)^ be
chained to slavish imitation of the building-s of his ancestors^
or be prevented from soaring* to a hig"her pitch by the dog-mas
of amateurs^ who can at the best obtain but a smattering-
of that art whose alphabet is^ unfortunately^ too easily
comprehended^ whose g-eneral form of words is too easily

recognised^ but the profundity of whose languag-e is proved
daily by the lack of originality and signal success^ in the
productions of its most deeply learned Students. It is time^
indeed^ that a change came over the spirit of the dream^ and
surely nothing in this age of progression will raise the
Architect but the production of original works. He must,
in shorty prove to the world_, that if in some cases there is
truth in the olden rhyme —

" ?Sj) line ant( rule, toovfe^ mang a foot/'

the opposite and more recent adage is applicable to him^
which states in answer that in the composition of such fools
the wise man predominates.

Independent^ however^ of the baneful effects of influence
from without^ there has been a division in the camp^ perhaps
more fatal to Architectural progression than the cause
stated ; and although the non-progressive feeling is greatly
changed by the spread of mechanical knowledg^e^ it is deeply
to be regretted that many of our Architects^ while admiring
the multifarious designs of medieval art^ have declared that
they were the result of mere chance^ little dreaming of the
mischief they were inflicting on their art. Chance^ indeed!
It had no more to do with design than it has now^ and the
sooner the notion is utterly discarded the better^ for it is only
by admitting at once^ and without reservation^ the fact of
mechanical foundations^ that we can ever rise to the creative
power^ — to that point where the mechanic ends and the
artist begins.

Briefly then^ but forcibly^ we may ask^ what is among the
chief merits apparent on the face of all the great compositions

12

of the old Masters in painting* and sculpture ? —that quality
requiring- to be attended to before they dared to attempt the
finish of their works ! Is it the existence of a particular
g-eometric figure^ or leading* line^ or is it otherwise ? Has
the existence and repetition of the triang*le^ the circle^ — the
og'ee^ or line of beauty^ — the radiation of lines and curves^ — or
the wonderful adaptation of mere vertical or horizontal lines
in their pictures^ and their sculptured g*roups^ nothing* to
do with the merits for which the world unconsciously admires
them? There is no possibility of g-iving* more than one
answer to the question^ and that is^ their undoubted founda-
tion upon principle.

If it cannot be denied that g-eometric laws are evident upon
the works of the painter and sculptor^ we may fairly ask the
objectors to their existence in architectural desig*n^ if the
common trefoil or quatrefoil of Gothic Architecture is or is
not Geometric ? Let any man who fancies the contrary^ try
to form them without the aid of compasses^ and he will be
speedily undeceived. Do the adversaries of order for one
moment doubt that the pointed arch of architecture is formed
of the arcs of circles ? They may just as well repudiate the
existence of the equilateral triang-le^ from the points of whose
base the first pointed arch was struck. As well mig-ht they
question the circular form of arches^ g*eneral previous to the
introduction of the pointed form ; we say introduction^ for
its orig'in is coeval with the first existence of g-eometry^ and
founded upon that fig*ure whose perfect form has been for
countless ag-es used as typifying* the unity of the Trinity.

Let the unbeliever in this matter g*o to any freemason and

13

ask^ if the equilateral triangle has anything to do with his

if

secret knowledge? Talk of working the forms appertaining
to Architecture^ by rule of thumb^ that is^ by hand^ and
without the aid of geometry^ forsooth ! It would be just as
absurd, just as unreasonable^ to ask the artificer to produce
good masonry without the use of the square^ or the plummet
and level. The mechanic would have too much common sense
to attempt such a gross breach of practical knowledge ; and
surely if this be the case^ those who claim to be his superior
as artists^ should at once and for ever discard the error.

The diagram chosen as the foundation of om* work^
contains perhaps more than any other geometric figure
the power of variation, and we have by no means exhausted
its fertility of change. Nay,
we can hardly be said to have
fairly opened out its vast, its
endless, powers of combination.
In its primary form it will at
once be universally recognised
as the kite star of the schoolboy,
the very first geometric figure
the child produces when playing
with a pair of compasses, by simply striking the radius
of a circle round its cu^cumference.

14

I

In its second form^ by the
lines cutting- through these
points on the circumference of
the circle^ and passing- throug-h
its centre^ we have the skeleton
of our diag-ram^ thus : —

The third form is the perfected
fig-ure upon which our desig-ns
are produced. It is simply the
introduction into the previous
figure of three equal circles in
contact.

We have a most remarkable coincidence^ and matter for
the consideration of the learned^ when we reflect that the
very first g-eometric figure^ formed intuitively by the child in
playing" with a pair of compasses^ marks in its prog-ress
a diag-ram^ known to the initiated as embodying- the

15

proftindities of masonic mysteries. The perfections of this
fig-m-e need no description^ for they are evident to the most
uneducated eye— but we may remind the reader that whether
we reg-ard it as formed by Hues or by curves^ and whether
these are represented as convex or concave^ the crafty symbol
patent over the whole world^ and during- all time^ still remains

the same. Our illustrations here are sufficient 3 but the reader
who wishes to investig-ate this matter further will find it fully
treated of in the 7th chapter of the fifth book of Vitruvius.

To those who have the knowledge of architectural detail^
our diag-rams and their results need no particular explanations^
but to the uninitiated it may be necessary to state^ that the
actual diag'ram^ or skeleton pattern^ exhibited upon the
succeeding" pag-es^ does not appear in the completed pattern^
being- a primary central line (a)^ used merely as a key

for placing' the expression of moulding-s upon it. So

16

a

m

soon then as the result appears this foundation line is
removed. We g'ive the sections of moulding-s applicable
to our desig'ns^ for all the varieties will apply correctly
as outlines^ althoug-h the light and shade^ from the
variety of contour^ would be very different. There may be^
however^ forms of moulding-s in which the central or pro-
jecting* line of the diag*ram appears —that is where the upper
member comes to a pointy thus. In particular situations this

form is effective^ but generally
speaking- the fillet on the top^
or nose^ as it is commonly called^
is by far the most pleasing in its
results.

After forming the lines of the diagram we proceed to
those indicated by the section^ above the line h. These
generally run unbroken^ through a composition as a frame-
workj while the portion below {h^ c)^ is continually separated
into minor detail. It is indeed to this beautiful arrange-
ment; to this exquisitely simple combination of primary and
secondary forms that medieval architecture owes the peculiar
charm — that projecting and recessing of parts which dis-
tinguishes it from more recent examples^ as essentially
containing the elements of the picturesque. And it is the
absence of this quality which marks so decidedly the failure of
nearly all modern attempts at imitation.

In a former work* upon another branch of our present

* " The Infinity of Greometric Design, by Eobert William Billings."
"William Blackwood and Sons. 1849,

subject it was stated that the object was " to carry one
diagram to what would appear the possible limits of its
varying" power." This diagram
is here exhibited^ and it may be
briefly stated^ that the power
of variation exists principally
in the enclosed spaces lying"
within the large circle^ and
between the four smaller ones
contained within it. Now^ if
we enlarge the enclosed circles these spaces become con-
tracted^ and so does the power of variation. As we carry
out this principle of enlarg"ement^ the field becomes smaller^
until at last when the circles nearly touch each other^ the
power of production has fairly ceased^ for it is only a few
peculiar combinations which are then producible. At least^
this conclusion is the author's result.

But carrying" the experiment further^ a result is given
totally differing" from the conclusion just formed^ for no
sooner are the enclosed circles made to come in contact than
a new and even greater power appears than that of our first
essay^ where^ as we have just stated^ the circles were discon-
nected^ and to this circumstance may be traced the orig-in
of the present series. As in the first series^ the secondary
foundation of desig"n in combination with four circles^ was
necessarily the square^ or the octag"on^ (two fig"ures ag"reeing"
in numbers with the primary diag"ram)^ so in the present effort
the secondary form^ in connection with the three inclosed
circles^ is the equilateral triang-le or the hexag"on. Now_,

c

18

every g-eometrical figure numbering- upward will be found^
upon the most cursory trial^ to contribute its quota to this
most easily accessible field of design^ of this inexhaustible
mine of linear development.

The truth of this g-eneral statement cannot be doubted; but
of all g-eometric forms^ the triangle as a foundation for
design possesses greater power of variation than any other
figure. Speaking of the circles here placed in connection
with this primary form^ we simply state^ that the power
of the combined diagram is materially contracted by them^
and by the larger circle enclosing the whole. Thus there is
frequently great difficulty in varying the small central tri-
angle formed by the junction of the enclosed circles^ and a
still greater difficulty in conquering' the monotony of the
spandrils on their outer boundaries; for it must be remem-
bered that the task we have proposed^ is^ in every design^ to
retain distinctly all the enclosing circle^ and all or the greater
part of those enclosed^ in order that the same framework
may be distinguished amidst the various expressions of form
arising from a common foundation.

Most extraordinary it is to watch the changes produced by
mere expression^ for although the same skeleton appears in
our whole collection^ nothing can be more different than the
results. It iS; in shorty with Tracery as with the human face^
and even lower in the scale of animal life. Every human
face has the same features in common^ but what a field of
contemplation — what wonderful variety does the mere
difference of individual expression present to us^ even if we
confine our observations to members of the same family.

They are, in fact, so many different designs, and woe to the
race of portrait painters were this state of affairs to be
chang-ed. Let the disbeliever ask any shepherd if he does
not know every one of his flock by their facial differences ?
We claim then for the patterns in our work, that the
variation of design upon the same diagram may be regarded
as so many modes of expression, or in fact as so many
varied faces having the same bones.

One glance at the collection of designs here presented will
convince the observer that none of the ordinary figures apper-
taining to Gothic Architecture have been used, excepting
indeed as perfectly subsidiary to the general form. Thus,
under the head of what has been usually termed design,
the three circles of our diagram might each have been
filled with a trefoil, a quatrefoil, a cinquefoil, and so
upward in number. Then, again, each of these figures
might have enclosed a foliated or other ornamental boss
in their centre, and the spandrils might have been varied
to an interminable extent by objects from the animal and
vegetable kingdom. But all these have been purposely
avoided, in order to prove the amount to be accomplished
with mere tracery, (a subject once supposed to be perfectly
exhausted), if we would but believe in the capability of
producing new combinations.

Foliage is here spoken of, as subservient to Tracery, but
foliated design upon geometric foundation was in extensive
use centuries before the invention of Gothic windows ^ and
that luxuriant display of form which has given such
imperishable interest to the buildings of the fourteenth and

c 2

so

fifteenth centuries^ was merely an offshoot from mechanical
foliation/ being" literally branches without leaves. But in
our present effort^ (intended only to facilitate the. student
in the use of mechanical principles) it was determined at
starting" to adhere strictly to mere framework^ leaving- all
attempts at leafwork utterly out of the question ; for as yet the
world is hardly prepared to admit even the g-eometric origin
of Tracerj^^ much less of the ornamental leaf work of Archi-
tecture^ although their originals^ — the very flowers of the
field^ have been impressed with this perfection of form by the
hand of the Great Creator. Let the sceptic examine the
simple daisy^ and if he be not convinced^ then let him turn
to the perfect g-eometric radiation of the cells of the sunflower.
They are only equalled in g-eometric perfection by the hex-
agonal cell of that most industrious insect architect the bee.

The leafy orig-in of Tracery is undoubted^ and is proved by
the terms of its own detail^ for what are its projecting- orna-
ments or points called? They are trefoil^ quatrefoil^ or
cinquefoil^ that is three-leaved^ four-leaved^ or five-leaved^
according- to the number of circles used in their formation^ as
the accompanying- fig-ures testify.

21

In some examples these points or foils are (by the close
proximity of the circles) very thin. But, numberless ancient
specimens prove^ that when the circles are smaller^ and^ conse-
quently^ more apart within the
space occupied by the whole
fig-ure^the points become broader.
When this occurs they are fre-
quently cut into the form of
leaves^ thus becoming- what their
name actually implies.

The mechanical practice of form is always important to
the artist^ because it makes him familiar with the correct
manipulation of detail. And if his knowledg-e on this head
becomes ultimately secondary to effect^ it should precede it^
for all works of art should bear examination in respect of
absolute correctness. If this merit be wanting-^ they are
indeed valueless^ excepting for mere show. Were there no
other advantag-e g-ained by the practice of mechanical desig-n
than the habit of calculation^ or the methodical spirit which it
eng-enders^ it is maintained that these would well repay both
the artist and the workman.

But there are other considerations^ and among- these^
especially to the Architect^ the studj^ of the g-eometric
ramifications of Tracery is the key to the restoration of
ancient examples^ of which time or wanton destruction has
but too frequently left us hardly so much of the skeleton
as would enable an architectural Cuvier to decipher and
declare the order. We may instance the numberless ruins
of ancient Churches^ of whose once g-org-eously traceried

22

windoAvs nothing* now remains^ save the stumps of their
severed branches. Yes ! to the initiated in the knowledg-e of
g*eometrical desig-n these shattered frag-ments are bones suf-
ficient to declare the skeleton^ — they are the leaves through
which the whole book may be read. By its means the
studies of the Architect may benefit art^ and create a new
fame for his predecessors^ by rescuing* their works from
oblivion.

The collection of Desig-ns following* this introductory Essay
may be reg*arded as experiments merely elementary^ upon
Tracery^ whose framework^ by the aid of mechanical diag*rams^
can be reproduced by any one capable of handling* a pair of
compasses. Nevertheless, they are not without interest to
those more advanced in art, as solving* much of the apparent
mystery which until recently enshrouded the ramifications of
a principal ornament in Gothic Architecture.

In a large number of Desig*ns, where each bears distinctly
a common foundation in the result, it must not be expected
that all the combinations can be equally successful. It
is fi^ankly admitted, that some are peculiar, and others may
be called 'even by a harsher name — but if the case be so
with the present series, it is equally so with many examples
having* only antiquity to recommend them. It is not to be
expected that every human face shall be regular in feature,
or what is termed pretty y but there may be a quality very
far superior — there may be the beauty of expression,
marking without doubt the lasting triumph of mind over
matter.

Our present attempt is presumed to be so many varia-

tions upon the same amount of material within the same
space^ that is to say^ it will g-enerally be found that each
design has nearly the same number of spaces within an
unvarying- framework. It is necessary to state this^ as a
reason for the absence of still g-reater chang-es than we
have shewn^ for by multiplying- the number of opening's
within a g-iven space^ or by reducing- them^ we should in
either case be walking- into another field of desig-n.

No difficulty can occur to the student in delineating- our
productions^ because each desig-n has its g-eometric diag*ram
placed upon the opposite pag-e^ with the curves and lines
of which they are composed^ numbered in the order of
formation^ and the "pons asinorum of Euclid thus needs
hardly to be passed in order to comprehend their formation.
Following- these diag-rams successively^ the student will find
that the mere delineation of one subject g-ives the clue to
other desig-ns ; and so rapidly do the sug-g-estions of varied
combinations press one upon another^ and^ apparently, almost
without mental effort^ that the subjects may almost be said
to come to hand ready desig-ned.

The application of a principle is surely no part of an
author's business. It is fit occupation for those directly
interested in the various productions or manufactures to
which his raw material may be made subservient^ but as
it is possible that the author of these productions may
ag-ain be asked the question^ Cui bono he deems it
rig-ht to say a few words by way of anticipation. He mig-ht^
indeed; shelter himself under the plea of the value of any
original contribution^ be it ever so humble, to our stores

24

of knowledge ; but there is not the shghtest occasion for
this unanswerable argument.

Briefly^ then^ his wish is to aid in destroying* that endless
repetition which disgraces our modern buildings^ expressed
sarcastically as the ^artificial infinite/ by proving that we
have the power of producing the reality of infinity.
Supposing^ (contrary to all modern practice) that a great
building had to be erected^ in which every window^ and
every ceilings the doors^ wall decorations^ screens and
furniture^ required not fifty^ but fifty thousand different
designs^ they could be produced by the aid of fixed diagrams.
Thus we have only to travel from the question of tracery^ to
take its framework as branches^ and then fit upon them the
leaves and blossoms of the vegetable kingdom. There will
be found the number at once^ each and all merely depending
upon the ability displayed^ as to whether they are or are not
to be classed as works of art.

Suppose^ again^ he recommends the application of his
designs to ornamental castings of all kinds^ or even the
adaptation of their principles to the framework of all kinds
of machinery^ for the flowing forms of medieval art can
be far more easily adapted to any change required for
strength^ than the set laws of classic architecture j and
besides this reason there is the desirableness of cultivating
our own nationality in art. Or turning to matters of
ordinary life^ let us ask^ Why should not a good circular
geometric pattern be as applicable for the decoration of a
common plate as that most extraordinary and far-famed
willow, or Chinese pattern, whose chief merit is, that it

contains more errors of Drawing* than those intention ally
displayed in Hog^arth's equally celebrated delineation of
Perspective Improved?

Objectors to works upon Architectural principles start up
at every point ; every step taken to elucidate them is at
once considered an innovation^ rather than an advantag-e^
and strangely enoug-h^ the enunciators are received with
marked suspicion^ as thoug-h they had some hidden
motive^ some undefinable and selfish object in view^ rather
than the desire of bring-ing* forward a simple truth.
Amongst other defects attributed to the present examples it
has been asserted that the desig'ns were made first^ and the
diag-rams then fitted to them — equivalent to the absurdity
of saying-^ that the manufactured article could be produced
before the raw material was provided. But; to be serious^ we
may at once affirm, that the results of Nature's operations
are displayed in the most beautiful patterns^ and these cannot
be delineated with certainty without fitting* them to a geometric
diagram^ whether we instance the rainbow^ the honey-comb^
the flowers of the field^ or the star-fish of the deep.

Further^ let it be asked^ where has our still increasing
store of knowledge regarding the principles of architecture
sprang from, if it be not from the mere fixing of diagrams^
which the result of investigation has proved to belong to
ancient exemplars — which the patient searcher has proved
to be the title-deeds of those vast estates of art we now
possess^ but whose descent to us is a mystery ; for
the secret working of the ancient freemasons^ once patent
all over Europe^ (as the universality of their productions

26

declare)^ was utterly lost during- the period of the Reforma-
tion^ when the glare of new lig*ht^ emanating* from the lamp
of relig-ious freedom^ effectually dimmed^ if it did not utterly
exting*uish^ the g-limmering* taper of architectural knowledg-e.

Perhaps enoug-h has been said to answer the objection
alluded to ; but there is another not yet stated^ which
affirms that the desig-ns belong' to the kaleidescope^ — a term
utterly inapplicable^ unless indeed the power of reproduction
may be said to equal that machine. Kaleidescope desig-ns
or patterns are purely mechanical — they are either so
many sectors of a circle^ or else so many radiations from
a common centre , and a g-lance will convince any person
with the slightest knowledg-c of Geometry^ that the present
Desig-ns are not at all of that class.

Supposing*^ for the sake of arg-ument^ it be admitted that
they were first designed^ and then reduced to a g-eometric
principle or calculation^ it is after all only the minor parts
to which the observation can possibly apply^ for all are
based upon one unvarying* foundation ; and this compels an
adhesion to g*eometric law^, from which there is no escaping*
in the g*eneral result.

Order^ in shorty is the foundation whence they
orig*inate^ and the pediment in which they terminate.

SlUstratintis.

III.

VII.

D 2

IX.

XIII.

I .

1

XIV.

XV.

The small unnumbered circles are repetitions of 7.

XVI.

1

The curves Nos. 1 and 4 are of similar radius.

XVII.

The curves 4 to 8 are all of one radius, that of the primaiy drcles.

XVIII.

■4

XIX.

XX.

XXI.

XXIII.

XXV.

XXVII.

XXVIII.

XXIX.

XXXI.

XXX li.

XXXIII,

The curves 1. to 4. are repetitions.

XXXV.

1

It is not the number of different curves used that always produces the best patterns ;
thus, the principal frame of this pattern is the repetition of the circles 1.

XXXVII.

F

XXXIX.

F 2

XLI.

XLII.

XLTII.

XLV.

XLVII.

This example is almost wliolly the repetition of one curve. Thus, Nos. 1
are all of equal radius.

XLIX.

LIII.

LVI.

In this example No. 2 is a repetition of 1, and 3 and 4 are equal circles In
minor tracery all the foil heads are repetitions of one circle.

U 2

LVIIo

I

i

NiimLors 1, 2, 3, are repetitions of one curve.

LTIU,

LIX.

1

i

Numbers 1, 2, and 3 are repetitions.

LX.

LXI.

I

LXUI.

The curves 4, 5, 6, 7, are repetitions of one radius.

I

LXTV.

LXVII.

I

LXVIII,

Tlie curves 2, .3, 4, ui'c repetitious.

LXIX.

1

LXX.

Here numbers 1 and 2 are of the same radius.

M

LXXI.

Number.-! 1 and 2 are similar, nnd so are numbers 3 and 4.

LXXIII.

LXXV.

Lxxvir.

eiicles Nos. 5 and 7 are equal.

LXXIX.

LXXX.

The curves 2 and 3 are repetitions.

LXXXI.

I

LXXXIII.

LXXXIV.

1

"L

Numbers G, 7, 8, are similar c.irves.

LXXXV.

Curves 1, 2, 3, 4, are the same curves , and 5, 6, are also equal.

LXXXIX.

The radius of curve 1 is the diameter of the outer circle.

XC,

/

/

/

The arcs 1, 2, are of the same radius ; and Nos. 4, 5, and 6, are also similar

XCI.

i

i

XCIII.

xcv.

I

The radius of Nos. 1,2, 3, is the diameter of the enclosing circle.

xcvi.

The radius of 3, 3, is the diameter of the outer circle.

of the same radius.

Nos. 4, 5, are curvea

XCVII.

XCVUI.

7|

Nos. 4, 5, 6, and 7, are circles of the same size.